已知存在M>0,使得对于任意的x∈D,有|f(x)|≤M,|g(x)|≤M
于是|f(x)±g(x)|≤|f(x)|+|g(x)|=2M
|f(x)g(x)|=|f(x)||g(x)|≤M²
从而可知f(x)±g(x),f(x)·g(x)在D上有界!